Given:
The radius of the cone = 14 ft
The slant height of the cone = 27 ft
To find the lateral surface area and the total surface area of the given cone.
Formula
The lateral surface area of the cone is
[tex]LSA = \pi rl[/tex] and
The total surface area of the cone is
[tex]TSA = \pi r^{2} + \pi r l[/tex]
where,
r be the radius and
l be the slant height of the cone.
Now
Taking r = 14 and l = 27 we get
[tex]LSA = \pi (14)(27)[/tex] sq ft
or, [tex]LSA = 1187.5[/tex] sq ft
Again,
[tex]TSA = \pi(14^2)+\pi (14)(27)[/tex] sq ft
or,[tex]TSA = 1803.3[/tex] sq ft
Hence,
The lateral surface area of the cone is 1187.5 sq ft and the total surface area of the cone is 1803.3 sq ft. Option C.
